Page 257 - Practical Design Ships and Floating Structures

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The wave exciting forces in the j-th bodies can be expressed by the incident wave potential and
diffraction potential.

3 TIME DOMAIN ANALYSIS
The equation of motion in the time domain can be derived by extending the equation for a floating
body proposed by Cummins(l962). In this method hydrodynamic forces are expressed by time
convolution of memory effect including wave damping effect and velocity of structure. VLFS is
assumed to be a pontoon-type barge with the length L, the breadth B and the draft d. The thin plate
theory can be used to describe vertical motions of it. The equation of motion can be given as follows.

2"
where, R& (t) = - jbh (0) cos(ot)da,
IC0
1"
a,,-(m)=a~/(o)+--lR~/(f)sin(rul)dr
00
M : structural mass matrix
a : added mass matrix
b : damping matrix
R : memory effects function
C : restoring force matrix
K : stiffness matrix
F : wave exciting force
Eqn. 15 can be solved by using the numerical integration technique in each time step and the Newmark
p method is employed here. To evaluate the retardation function, the wave damping coefficient
should be known. In order to predict hydroelastic responses of VLFS in irregular waves, the seaway is
represented by the ITTC spectrum.

A B
Ss = -exp(--)
w5 w4
where, A=172.75(H& IT:)
B=691.lTt
Hla : significant wave height
Tm : mean period
The wave amplitude of m-th component for irregular wave is obtained by Eqn. (21) and (22).